As the dedication in the stone indicates, this building on Victoria Street was once the Palatine Hotel, built in 1843 to provide accommodation in the vicinity of first Victoria and then Exchange Station. 

Beyond the hotel, on what was then Hunt's Bank, was the Palatine Buildings.  I don't know if they predate the hotel or were added later but they appear on the the map below dated 1844.

Below is a map of the area based on one drawn in 1888.

Today the Palatine belongs to Chetham's School of Music and is used by them for teaching spaces.  If you walk by you will hear music wafting out through the windows on Victoria Street.  As I write this in November of 2010, work is well underway to build a new school building on Hunt's Bank.  When it is complete, the Palatine will be demolished, opening up the view of the medieval buildings that accommodate the school and Chetham's Library.  The images below were taken in November of 2015.  The building was being wrapped in scaffolding prior to demolition.

As I said, the Palatine started life as a hotel but over the years it has gone through a number of changes in use.  It has been a large furniture store, a row of small shops and now a school.  If you click on the links below you can see images of it over the years.

19th Century

1925

1956

1962